ON MULTIDIMENSIONAL INVERSE SCATTERING UNDER THE TIME-DEPENDENT STARK EFFECT

Abstract

We study one of the multidimensional inverse scattering problems for quantum systems in time-dependent electric fields E (t ), whose leading part is represented as E₀ (1+|t |)^−𝜇, with 0 ≤ 𝜇 < 1, by utilization of the Enss–Weder time-dependent method. In our previous work, we have dealt with the case where E (t ) is a constant electric field. The present work is a continuation of that. The main purpose of this paper is to give an appropriate class of short-range potentials determined by the Enss–Weder time-dependent method, which is considered almost optimal also in terms of direct scattering problems.